Math  /  Trigonometry

QuestionFind the six trigonometric functions for the angle 3π4\frac{3 \pi}{4}. State "not defined" if applicable.

Studdy Solution
Calculate the values of the reciprocal trigonometric functions.
csc(3π4)=2\csc\left(\frac{3 \pi}{4}\right) = \sqrt{2}sec(3π4)=2\sec\left(\frac{3 \pi}{4}\right) = -\sqrt{2}cot(3π4)=1\cot\left(\frac{3 \pi}{4}\right) = -1So, the exact values of the six trigonometric functions of 3π4\frac{3 \pi}{4} aresin(3π4)=22\sin\left(\frac{3 \pi}{4}\right) = \frac{\sqrt{2}}{2}cos(3π4)=22\cos\left(\frac{3 \pi}{4}\right) = -\frac{\sqrt{2}}{2}tan(3π4)=1\tan\left(\frac{3 \pi}{4}\right) = -1csc(3π4)=2\csc\left(\frac{3 \pi}{4}\right) = \sqrt{2}sec(3π4)=2\sec\left(\frac{3 \pi}{4}\right) = -\sqrt{2}cot(3π4)=1\cot\left(\frac{3 \pi}{4}\right) = -1

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